Insulators or dielectrics are the media where signals propagate along the conductors of interconnects or transmission lines. Composite PCB and packaging dielectrics can be described with complex permittivity ∈=∈′−i·∈″ that exhibit strong dependency on frequency. Dielectric constant ∈′ and loss tangent
      tan    ⁢                  ⁢    δ    =            ɛ      ″              ɛ      ′      are changing substantially over the frequency band of multi-gigabit signal spectrum. Dispersive dielectric models are required from DC up to 20 GHz for 10-20 Gb/s signals, and up to 40 GHz for 20-40 Gb/s signals for meaningful electromagnetic modeling of interconnects.
Multi-line technique with the diagonalization of T-matrices was recently used by many authors [1]-[5] to extract complex propagation constants (Gamma) for transmission lines and to derive complex permittivity from it. The basis of the methods with Gamma is the fact that the diagonal T-matrix in the multi-line TRL de-embedding contains only elements defined by the complex propagation constant and independent of the transmission line characteristic impedance [6]. The major problem with all dielectric identification techniques based on Gamma extraction is high sensitivity to measurement noise and imperfections in the test structures. The most difficult part of all approaches based on Gamma is the solution of the hyperbolic equations with the measurement noise, geometrical imperfections and large errors when the length difference between the line segments is half of wavelength. Identification of the propagation constant over a wide frequency band may require more than two line segments and additional short and open structures as suggested in [4]. In addition, even strip-line configurations do not provide an easy way to extract the propagation constant because of the dependency of Gamma on the conductor loss and dispersion, conductor roughness and high-frequency dispersion due to in-homogeneity of the dielectric layers adjacent to the strip in the PCB applications. The high-frequency dispersion is even more critical in cases if micro-strip structures are used for the identification (micro-strip structures may have advantage due to simpler transitions from probes or coaxial lines). Approximate formulas used to convert Gamma into dielectric constant may lead to different types of defects—such as overestimated loss tangent due to not accounting for the conductor roughness or plating. It means that simplified formula-based models or static and quasi-static solutions are practically useless above 3-5 GHz both for the dielectric parameters identification and for the compliance analysis. Here we use 3D full-wave electromagnetic analysis to compute generalized modal S-parameters of a line segment with all types of conductor and dielectric losses and dispersion included. The dielectric model is derived by comparison of the measured and computed generalized modal S-parameters. The proposed procedure is much less sensitive to the measurement noise and to geometrical differences between the samples.